Many studies on skill acquisition have claimed that improvements in performance follow the power law of practice. However, it is also well-known that during long-term practice there are fluctuations such as plateaus, regressions, and spurts. In order to objectively examine the fluctuations in learning process, we analyzed a long-term learning process in a simple assembly task. We applied a time-series analysis based on the state space method to the task completion time. The analysis revealed that the power law of practice provided only a first approximation, and that fluctuations around the power law line reflected long-term trends. Next, we focused on one of the fluctuations, and carried out cognitive analysis to find what produced the fluctuation. We found that, contrary to the dominant skill acquisition model, the slump was attributable to the mismatch between the level of skills and the environment that the skills are demonstrated in. This analysis suggests that, in order to fully elucidate the processes and mechanisms of skill acquisition, attention should be paid not only to the internal mechanisms, but also to the external environment that the skills are demonstrated in. We discussed the above results in terms of the essential role of fluctuations and environment in skill learning as well as the nature of the data obtained from a single subject.